# University of Twente Student Theses

## Extended self similarity in Rayleigh-Bénard convection

Franken, A.D.
(2017)
*Extended self similarity in Rayleigh-Bénard convection.*

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Abstract: | The scaling behavior of the normalized even order structure functions S_2p(r)=<(u(x + r) - u(x))^(2p)> ^(1/p) in various configurations of Rayleigh-Bénard (RB) convection is studied. Here u is a velocity component orthogonal to gravity, and x is the spatial coordinate component in the same direction. It is known that for shear driven wall-bounded flows, the longitudinal structure functions can be described by the self similar profile S_2p ~ D_p ln(r/y) + E_p in the logarithmic region, where y is the wall normal height and D_p and E_p are constants. In line with the extended self similarity hypothesis, it was recently shown that the ratios D_p/D_1 appear more universal. These ratios are extracted from plots between structure functions and show agreement for various shear flows. In this report, the above observations are tested for rectangular periodic RB convection cells with a width up to 64 times larger than the distance between the bottom and top wall. The self similar profile could not be observed for any of the different Raleigh number cases. The ratios D_p/D_1 however could clearly be found from the structure functions in the energy containing region of r. The values of D_p/D_1 were found not to be independent of wall normal distance. Compared to the previously found values in the logarithmic layer of shear flows, the ratios are lower near the bottom wall, and higher near the half height plane for RB convection. These results appear to be independent of the Rayleigh number in the range Ra = 10^7 - 10^9. |

Item Type: | Essay (Bachelor) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 31 mathematics, 33 physics |

Programme: | Applied Mathematics BSc (56965) |

Link to this item: | https://purl.utwente.nl/essays/73946 |

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